On a risk model with randomized dividend-decision times

Zhimin Zhang

doi:10.3934/jimo.2014.10.1041

Article Contents

2014, Volume 10, Issue 4: 1041-1058. Doi: 10.3934/jimo.2014.10.1041

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On a risk model with randomized dividend-decision times

Zhimin Zhang^1,

1.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331

Received: September 30, 2012

Revised: November 30, 2013

Published: September 2014

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Abstract

In this paper, we consider a perturbed compound Poisson risk model with a randomized dividend strategy. Assume that decisions on paying off dividends are made at some random observation times. Whenever the observed value of the surplus process exceeds a given barrier $b$, the excess value will be paid off as dividends. We assume that the Laplace transform of the individual claim size belongs to the rational family. When the time intervals between successive decision times follow exponential distribution, we present explicit expressions for the Gerber-Shiu function. We also extend the exponential assumption to Erlang and discuss the solution procedure.

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Mathematics Subject Classification: Primary: 91B30; Secondary: 62P05.

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